The consecutive odd primes, such as 11 and 13 are, are called a pair of "twin primes". How many pairs of twin primes are there between 15 and 45.

Solution :

17 and 19 - Twin primes

29 and 31 - Twin primes

41 and 43 - Twin primes

Hence there are 3 twin primes lies between 15 and 45.

(A) 2 (B) 3 (C) 4 (D) 5 (E) 7

Question 15 :

For any number x, the symbol ⌈x⌉ means the smallest integer that is greater than or equal to x. For examples ⌈3.2⌉ is 4. what is √156.3

Solution :

⌈3.2⌉ = 4

√156.3 = ⌈12.51⌉ = 13

Hence the answer is 13.

Question 16 :

Eight years from now, Oana will be twice as old as her brother is now. Oana is now 12 years old. How old is her brother now ?

Solution :

Let "x" be Oana's brother's present age

After 8 years :

Oana's age + 8 = 2x

12 + 8 = 2x

2x = 20

x = 20/2 = 10 years

Question 17 :

Suppose a snail crawls 2/5 inch per second. At this rate, what is the total number of inches the snail crawls in 2 minutes ?

Solution :

2 minutes = 120 seconds

Number of inches the snail crawls = 120 (2/5)

= 24 (2)

= 48 inches

Question 18 :

The straight line graph shows the relationship between the number of tickets sold and amount of money in the cash register if the register contained $150 before any tickets were sold. What is the price of 1 ticket.

x axis = no of tickets sold, y axis in cash register

Solution :

Cost of 1 ticket = "x"

30 x = 600

x = 600/30

x = 20

Question 19 :

If 15 - 2x <7, then for all possible values of x that make the inequality true.

Solution :

15 - 2x <7

Subtract 15 on both sides

-2x < 7 - 15

-2x < -8

Divide both sides by -2.

x > 4 (Since we divide by negative sign, the inequality sign will get changed).

Question 20 :

Four congruent circles are enclosed in a square as shown. The perimeter of the square is 64. What is the circumference of one of the circles (in terms of π)

Solution :

Perimeter of square = 64

4a = 64

a = 64/4 = 16

Diameter of two circles = 16

Diameter of one circle = 8

radius of circle = 4

Area of 4 circles = πr2

= π(4)2

= 16π

Hence the area of 4 circles is 16π.

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